Update rules and interevent time distributions: Slow ordering versus no ordering in the voter model

Fernández-Gracia, Juan; Eguı́luz, Vı́ctor M.; Miguel, M. San

doi:10.1103/physreve.84.015103

Cited by 62 publications

(84 citation statements)

References 30 publications

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“…In physical terms, the states of the interacting particles are coupled to the state of the field that carries the interaction. Another possible avenue of research is the addition of more realistic features to the model, such as the temporal patterns of human interactions [26,27], which introduces heterogeneity in the activation of different links.…”

Section: Summary and Discussionmentioning

confidence: 99%

Dynamics of link states in complex networks: The case of a majority rule

et al. 2012

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Motivated by the idea that some characteristics are specific to the relations between individuals and not to the individuals themselves, we study a prototype model for the dynamics of the states of the links in a fixed network of interacting units. Each link in the network can be in one of two equivalent states. A majority link-dynamics rule is implemented, so that in each dynamical step the state of a randomly chosen link is updated to the state of the majority of neighboring links. Nodes can be characterized by a link heterogeneity index, giving a measure of the likelihood of a node to have a link in one of the two states. We consider this link-dynamics model in fully connected networks, square lattices, and Erdös-Renyi random networks. In each case we find and characterize a number of nontrivial asymptotic configurations, as well as some of the mechanisms leading to them and the time evolution of the link heterogeneity index distribution. For a fully connected network and random networks there is a broad distribution of possible asymptotic configurations. Most asymptotic configurations that result from link dynamics have no counterpart under traditional node dynamics in the same topologies.

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Section: Summary and Discussionmentioning

confidence: 99%

Dynamics of link states in complex networks: The case of a majority rule

et al. 2012

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“…The herding voter model introduced in [15] takes into account simultaneously heterogeneous populations where agents are given intrinsic activity rates {λ i } [16,17] accounting for the rate at which agents interact with their peers-and arbitrary influences of agents on each other. This is modeled through the probability Prob(j|i) that agent i copies the opinion of agent j when i is activated at rate λ i .…”

Section: The Herding Voter Modelmentioning

confidence: 99%

“…where ξ i (t) and φ i (t) are random dichotomous variables that take values: ξ i (t) = 1 with probability λ i dt 0 with probability 1 − λ i dt (17) and φ i (t) = 1 with probability i dt 0 with probability 1 − i dt…”

Section: The Herding Voter Model With Noisementioning

confidence: 99%

Dynamical properties of the herding voter model with and without noise

Rozanova

Boguñá

2017

Phys. Rev. E

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Collective leadership and herding may arise in standard models of opinion dynamics as an interplay of a strong separation of time scales within the population and its hierarchical organization. Using the voter model as a simple opinion formation model, we show that, in the herding phase, a group of agents become effectively the leaders of the dynamics while the rest of the population follow blindly their opinion. Interestingly, in some cases such herding dynamics accelerates the time to consensus, which then become size independent or, on the contrary, makes the consensus nearly impossible. These new behaviors have important consequences when an external noise is added to the system that makes consensus (absorbing) states to disappear. We analyze this new model which shows an interesting phase diagram, with a purely diffusive phase, a herding (or two-states) phase, and mixed phases where both behaviors are possible.

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“…Masuda et al investigated the effect of heterogeneity in the flip-rates of agents [17]. While they have some spirit in common, the present model differs from other time dependent models including such effects as latency or ageing of states [18,19,20] in that the change in flip rate doesn't depend on the opinion or the time of adoption of the opinion. That is, we are not interested in ageing of the opinions but of the agents themselves.…”

Section: Introductionmentioning

confidence: 99%

A voter model with time dependent flip rates

Baxter¹

2011

J. Stat. Mech.

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Abstract. We introduce time variation in the flip-rates of the Voter Model. This type of generalisation is relevant to models of ageing in language change, allowing the representation of changes in speakers' learning rates over their lifetime. and may be applied to any other similar model in which interaction rates at the microscopic level change with time. The mean time taken to reach consensus varies in a nontrivial way with the rate of change of the flip-rates, varying between bounds given by the mean consensus times for for static homogeneous (the original Voter Model) and static heterogeneous flip-rates. By considering the mean time between interactions for each agent, we derive excellent estimates of the mean consensus times and exit probabilities for any time scale of flip-rate variation. The scaling of consensus times with population size on complex networks is correctly predicted, and is as would be expected for the ordinary voter model. Heterogeneity in the initial distribution of opinions has a strong effect, considerably reducing the mean time to consensus, while increasing the probability of survival of the opinion which initially occupies the most slowly changing agents. The mean times to reach consensus for different states are very different. An opinion originally held by the fastest changing agents has a smaller chance to succeed, and takes much longer to do so than an evenly distributed opinion.

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Update rules and interevent time distributions: Slow ordering versus no ordering in the voter model

Cited by 62 publications

References 30 publications

Dynamics of link states in complex networks: The case of a majority rule

Dynamics of link states in complex networks: The case of a majority rule

Dynamical properties of the herding voter model with and without noise

A voter model with time dependent flip rates

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